Here is the full list of all 50 Marvel's Spider-Man: Miles Morales trophies - there are 37 bronze, 10 silver, 2 gold and 1 platinum.
Complete an Enemy Base without being detected
Shut down all Underground Hideouts
Get Spectacular or better in a Spider-Training Stealth Challenge
Defeat 50 enemies while Camouflaged
Get Spectacular or better in a Spider-Training Traversal Challenge
Unravel a criminal conspiracy in Harlem
Defeat 100 enemies with Venom attacks
Perform 100 Stealth Takedowns
Get Spectacular or better in a Spider-Training Combat Challenge
Scroll through the entire Social Feed at the end of the story
Save Harlem
Walk through Miles and Phin's past
Beat Phin at the rocket launch mini-game
Defeat Prowler
Defeat Roxxon Rhino
Use Venom Dash to throw an enemy into a group of three or more
Chase Tinkerer through the city
Complete the vault sequence in Underground Undercover
Perform a 100x Combo
Investigate Roxxon's underground lab
Keep the bridge together
Craft a Suit Mod
Get the trains running again
Receive the Gift Suit
Ride Rhino through the mall
Smash into 15 breakable objects while steering Rhino through the shopping mall
Collect all Trophies
Unlock all Skills
100% complete all districts
Collect all Time Capsules
Collect all Postcards
Open all Underground Caches
Shut down all Roxxon Labs
Purchase all suits
Complete every Spider-Training Challenge once
Complete the Final Test
Craft 10 Upgrades
Collect all Sound Samples and recreate the Davis Brothers Mix
Perform 25 Ceiling Takedowns
Perform 25 Wall Takedowns
Perform a Venom Jump, then a Venom Dash on a single enemy
Pay your respects to a legend in the Upper West Side
Apply a sticker and customize lighting while in Photo Mode
Defeat 50 enemies with Remote Mine gadget
Complete all FNSM app requests
Craft a Visor Mod
Pay respects at Jefferson Davis' grave in Harlem
Complete all Bonus Objectives for every crime type
Ride the derelict boat in southern Chinatown
Complete the game on New Game+